Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-7x-3y &= -6 \\ -8x-6y &= -6\end{align*}$
Answer: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-8x = 6y-6$ Divide both sides by $-8$ to isolate $x$ $x = {-\dfrac{3}{4}y + \dfrac{3}{4}}$ Substitute this expression for $x$ in the first equation. $-7({-\dfrac{3}{4}y + \dfrac{3}{4}}) - 3y = -6$ $\dfrac{21}{4}y - \dfrac{21}{4} - 3y = -6$ Simplify by combining terms, then solve for $y$ $\dfrac{9}{4}y - \dfrac{21}{4} = -6$ $\dfrac{9}{4}y = -\dfrac{3}{4}$ $y = -\dfrac{1}{3}$ Substitute $-\dfrac{1}{3}$ for $y$ in the top equation. $-7x-3( -\dfrac{1}{3}) = -6$ $-7x+1 = -6$ $-7x = -7$ $x = 1$ The solution is $\enspace x = 1, \enspace y = -\dfrac{1}{3}$.